Sine wave multiplication circuit and sine wave multiplication method

ABSTRACT

A sine wave multiplication circuit multiplies an analog input signal by n (n is an integer equal to or greater than 2) weighting coefficients each having a unique value. The polarity of the analog input signal multiplied by one of the n weighting coefficients is changed over. Further, changeover among the n weighting coefficients and of the polarity is performed after every sampling period equal to ½k (k is an integer, and 2k is equal to or greater than 6 but equal to or smaller than 4n) of one period of the sine wave signal by which the analog input signal is multiplied. As a result, a staircase waveform having 2n positive and negative stairs is generated while unnecessary harmonic wave components in the proximity of the sine wave signal by which the analog input signal is multiplied can be reduced.

BACKGROUND OF THE INVENTION

This invention relates to a sine wave multiplication circuit and a sinewave multiplication method for multiplying a certain analog signal by asine wave signal, and more particularly to an analog sine wavemultiplication circuit and an analog sine wave multiplication method fora sine wave signal.

It is one of the most basic functions in various signal processes tomultiply a certain signal by a sine wave. For example, in frequencyconversion of shifting a certain signal by a desired frequency, a sinewave multiplication circuit is required. Further, a sine wavemultiplication circuit is required essentially also for conversion of afrequency band of a signal into a frequency band in the proximity ofzero (direct current) in frequency in order to detect an arbitraryfrequency component of the signal.

Here, for example, taking arithmetic operation for determination of anaccurate sum of two sine waves as an example, arithmetic operation ofe ^(j(ω1t+θ1)) ·e ^((ω2t+θ2)) =e ^(j{(ω1+ω2)t+θ1+θ2})  (1)is examined.

Actually, in order to determine the real part of the expression (1)above, arithmetic operation given by the following expression (2) shouldbe performed:Cos(ω1 t+θ1)·Cos(ω2 t+θ2)−Sin(ω1 t+θ1)·Sin(ω2t+θ2)=Cos{(ω1+ω2)t+θ1+θ2}  (2)

The expression (2) above can be implemented, for example, by two analogmultiplication circuits. The multiplication circuit used here is calledGilbert multiplier and is disclosed in BARRIE GILBERT, “A PreciseFour-Quadrant Multiplier with Subnanosecond Response”, IEEE JOURNAL OFSOLID-STATE CIRCUITS, Vol. SC-3, No. 4, December 1968, pp. 365-373(hereinafter referred to as Non-Patent Document 1). A circuitconfiguration of the Gilbert multiplier is shown in FIG. 23.

However, a high degree of accuracy in arithmetic operation cannot beanticipated with such an analog multiplier as described above. The mostserious problem is an offset. Transistors of the Gilbert multiplier ofFIG. 23 involve mismatching in characteristic. As a result, an offsetvoltage is superposed equivalently on each of four input signals to theGilbert multiplier of FIG. 23. As a result, a feed-through phenomenonthat the components appear as they are on the output occurs. Further, ifthe two multiplication circuits 101 and 102 have mismatching in gain,then not only a component of the sum of frequencies ω1 and ω2 but alsoanother component of the difference between the frequencies ω1 and ω2,that is, an image component, appear on the output.

The components can be described in connection with a signal spectrumillustrated in FIGS. 24A and 24B. The output (b) with regard to signalsω1 and ω2 of the input (a) exhibits, in addition to a desired signal ofthe signal ω1+ω2, feed-through values of the input signals ω1 and ω2themselves and an image component of the signal ω1−ω2. This is caused byoffset voltages of the analog multiplication circuits and a gain errorbetween the two multiplication circuits 101 and 102.

The feed-through matters particularly. The Gilbert multiplier shown inFIG. 23 has such a narrow dynamic range of an input thereto that, inorder to use the Gilbert multiplier in a linear region, only a signal ofan amplitude of approximately 10 to 20 m Vp−p can be inputted. Incontrast, the offset voltage of transistors usually is approximately 1mV. Accordingly, the feed-through can be suppressed only byapproximately −20 dB of the desired signal. In order to further reducethe feed-through, special measures (for example, trimming) in layout orcircuit design are required. Even though, it is considerably difficultto assure −40 dB.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a sine wavemultiplication circuit and a sine wave multiplication method which canachieve reduction of the feed-through and an image component.

In order to attain the object described above, according to an aspect ofthe present invention, there is provided a sine wave multiplicationcircuit for multiplying an analog signal by a sine wave signal,comprising a weighting section having n weighting coefficient eachhaving a unique value for multiplying the analog input signal by theweighting coefficients, n being an integer equal to or greater than 2, apolarity changeover section for changing over the polarity of the analoginput signal outputted from the weighting section after multiplied byone of the n weighting coefficients, and a control section forperforming changeover among the n weighting coefficients and changeoverof the polarity after every sampling period equal to ½k of one period ofthe sine wave signal by which the analog input signal is multiplied, kbeing an integer, 2k being equal to or greater than 6 but equal to orsmaller than 4n.

According to another aspect of the present invention, there is provideda sine wave multiplication method for multiplying an analog signal by asine wave signal, comprising a first step of multiplying the analoginput signal by n weighting coefficient each having a unique value, nbeing an integer equal to or greater than 2, a second step of changingover the polarity of the analog input signal multiplied by one of the nweighting coefficients, and a third step of performing changeover amongthe n weighting coefficients and changeover of the polarity after everysampling period equal to ½k of one period of the sine wave signal bywhich the analog input signal is multiplied, k being an integer, 2kbeing equal to or greater than 6 but equal to or smaller than 4n.

In the sine wave multiplication circuit and the sine wave multiplicationmethod, the number of weighting coefficients by which the analog inputsignal is to be multiplied is set to n, and the weighting coefficient tobe used for the multiplication and the polarity of the weightingcoefficient are changed over after every sampling period such that astaircase waveform having 2n positive and negative stairs is generated.In other words, the sine wave signal by which the analog input signal isto be multiplied becomes equivalent to a staircase wave. Consequently,unnecessary harmonic waves in the proximity of the sine wave signal usedfor the multiplication are suppressed to very low levels. Further, wherethe circuit for generating the sine wave signal is configured such thatthe n weighting coefficient are set and the weighting coefficient andthe polarity are changed over, it can be formed from a resistor networkand switch elements for determining the weighting coefficients.Consequently, the offset and the error in coefficient are very smallwhen compared with those of an alternative sine wave multiplicationcircuit which is formed using transistors.

With the sine wave multiplication circuit and the sine wavemultiplication method, since the sine wave signal by which the analoginput signal is multiplied is equivalent to a staircase wave,unnecessary harmonic waves in the proximity of the sine wave signal usedfor the multiplication can be suppressed to very low levels.Consequently, an analog multiplication result of a very high degree ofaccuracy having a very small feed-through or image component can beobtained.

The above and other objects, features and advantages of the presentinvention will become apparent from the following description and theappended claims, taken in conjunction with the accompanying drawings inwhich like parts or elements denoted by like reference symbols.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a basic configuration of a sine wavemultiplication circuit to which the present invention is applied;

FIG. 2 is a timing chart illustrating circuit operation of the sine wavemultiplication circuit of FIG. 1;

FIG. 3 is a waveform diagram illustrating the necessity for acoefficient to satisfy a certain condition;

FIG. 4 is a diagram illustrating weighting coefficients at differenttime units;

FIG. 5 is a diagram illustrating spectra of the weighting coefficients;

FIG. 6 is a diagram illustrating spectra of harmonic components of anactual weighting coefficient;

FIG. 7 is a block diagram of an example of the sine wave multiplicationcircuit having a configuration wherein n=4;

FIG. 8 is a waveform diagram illustrating an output waveform andweighting coefficients a different times of the sine wave multiplicationcircuit wherein n=4;

FIG. 9 is a diagram illustrating an output spectrum of the sine wavemultiplication circuit wherein n=4;

FIG. 10 is a waveform diagram illustrating sampling points which includea maximum value and an output waveform of the sine wave multiplicationcircuit;

FIG. 11 is a similar view but illustrating sampling points and theoutput waveform of the sine wave multiplication circuit where thesampling points are selected including a zero cross but not including amaximum point;

FIG. 12 is a similar view but illustrating an output waveform of thesine wave multiplication circuit where the sampling points are selectedwithout including any of a maximum point and a zero cross;

FIG. 13 is a similar view but illustrating the output waveform of thesine wave multiplication circuit where the sampling points are selectedincluding both of a maximum point and a zero cross;

FIG. 14 is a circuit diagram showing an example of a weighting circuitand a polarity changeover circuit of the sine wave multiplicationcircuit;

FIG. 15 is a waveform diagram illustrating control of switches andweighting coefficients of the weighting circuit and the polaritychangeover circuit of FIG. 14;

FIG. 16 is a circuit diagram showing another example of the weightingcircuit and the polarity changeover circuit of the sine wavemultiplication circuit;

FIG. 17 is a waveform diagram illustrating control of switches andweighting coefficients of the weighting circuit and the polaritychangeover circuit of FIG. 16;

FIG. 18 is a circuit diagram showing a further example of the weightingcircuit and the polarity changeover circuit formed using a buffercircuit equivalently having an input switch function;

FIG. 19 is a circuit diagram showing an example of a configuration ofbuffer amplifier with an input switch function of the sine wavemultiplication circuit;

FIG. 20 is a circuit diagram showing a sine wave generation circuit towhich the sine wave multiplication circuit is applied;

FIG. 21 is a block diagram showing a multiplication circuit to which thesine wave multiplication circuit is applied;

FIG. 22 is a waveform diagram illustrating a complex signal whichincludes a desired signal at a frequency and includes a disturbancesignal at another frequency;

FIG. 23 is a circuit diagram showing a conventional complexmultiplication circuit by a multiplication circuit (Gilbert multiplier);and

FIGS. 24A and 24B are diagrams illustrating a signal spectrum offeed-throughs and an image component.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, there is shown a basic configuration of a sine wavemultiplication circuit to which the present invention is applied.

The sine wave multiplication circuit shown includes n coefficientcircuits 11-1 to 11-n for multiplying an analog input signal vin(t) by ncoefficients m1 to mn each having a unique value, n coefficientselection switches 12-1 to 12-n for selecting the coefficient circuits11-1 to 11-n, respectively, and a polarity changeover circuit 13 forchanging over the polarity of an analog signal outputted from one of thecoefficient selection switches 12-1 to 12-n. The sine wavemultiplication circuit further includes a pulse generation circuit 14serving as a control section for changing over the selection of thecoefficient circuits 11-1 to 11-n (selection of the analog input signalmultiplied by one of the n coefficients m1 to mn) and the polarity ofthe polarity changeover circuit 13 after every sampling period equal to½k (k is an integer, 2k being equal to or higher than 6 but equal to orlower than 4n) of the cycle of the sine wave signal by which the analoginput signal vin(t) is to be multiplied.

In the sine wave multiplication circuit, the n coefficient circuits 11-1to 11-n and the n coefficient selection switches 12-1 to 12-n form aweighting circuit 10. The number n of the n coefficient circuits 11-1 to11-n is at least 2. The polarity changeover circuit 13 includes aninverting amplifier 131 having a gain of −1, and a path changeoverswitch 132 for changing over between a path which includes the invertingamplifier 131 and another path which does not include the invertingamplifier 131. The pulse generation circuit 14 generates pulse signalsS1 to Sn and SP for controlling the coefficient selection switches 12-1to 12-n and the path changeover switch 132 to change over in response toa predetermined clock, respectively. The polarities of the weightingcoefficients (unique values) of the coefficient circuits 11-1 to 11-nand the polarity changeover circuit 13 are set such that the products ofthe weighting coefficients and the polarities after changeover for eachone sampling period increase in proportion to instantaneous values ofthe sine wave signal at instantaneous times for each sampling period.

Now, circuit operation of the sine wave multiplication circuit accordingto the present embodiment having the configuration described above isdescribed with reference to a timing chart of FIG. 2. Here, a casewherein two coefficient circuits 11-1 and 11-2 are provided is examinedas the simplest example of the sine wave multiplication circuit.

The polarity changeover circuit 13 assumes the positive polarity(coefficient 1) within a period of time from t0 to t4 and then assumesthe negative polarity (coefficient −1) within another period of timefrom t4 to t8. The coefficient selection switch 12-1 exhibits an on(closed) state within a period of time from t1 to t3 and another periodof time from time t5 to t7, and the coefficient selection switch 12-2exhibits an on state within a period of time from t3 to t5 and anotherperiod of time from t7 to t9. Thereafter, the coefficient selectionswitches 12-1 and 12-2 repeat the on states described above. As aresult, the time variation of the weighting coefficient mo(t) withrespect to the analog input signal vin(t) becomes such as illustrated inFIG. 2. The weighting coefficient mo(t) can exhibit four coefficients ofm1, m2, −m1 and −m2.

The coefficients m1 and m2 and the coefficients −m1and −m2 must satisfycertain conditions. FIG. 3 illustrates the conditions just mentioned.Referring to FIG. 3, the coefficients m1 and m2 and the coefficients of−m1 and −m2 must increase in proportion to instantaneous values of thesine wave signal when 4n sampling points are selected at equal intervalswithin one cycle of the sine wave signal symmetrically with respect totime ty of a peak value of the sine wave signal without including thetime ty. In other words, the 4n sampling points are selectedsymmetrically with respect to a zero-cross point tx.

The weighting coefficient mo(t) at a time unit ti is a sample obtainedby sampling the sine wave signal as seen in FIG. 4. Where n coefficientcircuits 11 are involved, 2n weighting coefficients mo(t) are obtainedincluding positive and negative weighting coefficients. Since eachweighting coefficient is used twice within one cycle, the sine wavesignal is sampled by 4n times within one cycle. Since n=2 in the presentexample, the weighting coefficients involved are obtained by samplingthe sine wave signal by 8 times. Where the spectrum of the weightingcoefficients mo(t) of FIG. 4 is considered, such a spectrum asillustrated in FIG. 5 is obtained. Where the frequency of the sine wavesignal is represented by f, since the sine wave signal is sampled by 8f,a desired signal exists at f, and a spectrum exists at 7f and 9f.Nothing exhibits between f and 7f.

The actual weighting coefficients mo(t) do not exhibit a samplingwaveform represented by a δfunction (impulse train) but exhibits astaircase waveform obtained by first order holding of the samplingwaveform. Harmonic components at this time have such a spectrum asillustrated in FIG. 6 because attenuation (Sinx/x) by a well-knownaperture effect is applied to the harmonic components. The seventh-orderharmonic component attenuates approximately by 17 dB, and theninth-order harmonic component attenuates approximately by 19 dB. Sincethe seventh- and ninth-order harmonic components are spaced considerablyfrom the basic wave, they can be attenuated considerably by passing themthrough a simple low-pass filter. The weighting coefficients m1 and m2are determined setting the amplitude of the sine wave signal to be usedfor multiplication to 1.

Since time t0 in FIG. 3 is π/8, m2=Sin(π/8)=0.383. Meanwhile, since timet1 is 3π/8, m1=Sin(3π/8)=0.924. If the coefficient circuit number n isincreased, then unnecessary harmonic waves of the sine wave signal to beused for multiplication can be pushed aside toward a higher frequencyband and hence be reduced in level.

FIG. 7 shows an example of a configuration of the sine wavemultiplication circuit where n=4. FIG. 8 illustrates an output waveformof the sine wave multiplication circuit of FIG. 7 and weightingcoefficients mo(t) at different times.

As seen in FIG. 8, the output of the sine wave multiplication circuit ofFIG. 7 exhibits a staircase waveform having eight values (m1 to m4 and−m1 to −m4) and is obtained by sampling the sine wave signal by 16times. Where the amplitude of the sine wave signal to be used formultiplication is represented by 1, the weighting coefficients m1 to m4have such values as given below. In particular, m4=Sin(n/16)=0.195,m3=Sin(3π/16)=0.556, m2=Sin(5π/16)=0.831, and m1=Sin(7π/16)=0.981. FIG.9 illustrates an output spectrum where n=4. Although the attenuation ofharmonic components is approximately 6 dB, since the harmonic componentsare the fifteenth- and seventeenth-order harmonic components havingfrequencies substantially equal to twice, they can be attenuated using avery simple filter.

Now, requirements in sampling of a sine wave signal by the sine wavemultiplication circuit of the present embodiment are described.

In the sine wave multiplication circuit of the present embodiment, oneweighting coefficient is basically used twice in one cycle. Further, thenumber of sampling points must be an even number because positive andnegative portions of the sine wave signal are sampled symmetrically. Inthe following description, the number of sampling points in one halfcycle is represented by k. k=2, that is, four-time sampling, isbasically meaningless. In four-time sampling, a reflected spectrumappears at the three-time sampling point and a third-order harmonic waveis generated, and therefore, no essential difference appears from arectangular wave. The smallest sampling number k with which the presentinvention is significant is k=3, that is, 6 times.

Where k is an odd number (sampling number 2k=6, 10, 14, . . . ), thesampling points include one of a maximum value and a zero cross. 2k=4 isexcepted because it is smaller than 6. FIG. 10 shows sampling pointsincluding a maximum value and an output waveform. In this instance,n=k/2+0.5. A peak weighting coefficient is used twice within one cyclewhile the other weighting coefficient is used four times. FIG. 11 showssampling points and an output waveform when sampling points including azero cross are selected. In this instance, n=k/2+0.5. The weightingcoefficient of zero is used twice within one cycle while the otherweighting coefficient is used four times. The two cases do not have anessential difference while only the sampling points are differentbetween them. It may be safely said that, since the sampling points ofFIG. 11 include a zero cross, one of the weighting coefficients is zeroand there is a merit that the substantial number of weightingcoefficient circuits decreases.

Now, a case wherein k is an even number (sampling number 2k=8, 12, 16, .. . ) is examined. 2k=4 is excepted because it is lower than 6. Also inthis instance, two arrangements of sampling points are available. FIG.12 shows sampling points and an output waveform when the sampling pointsare selected so as not to include any of a maximum value and a zerocross. In this instance, n=k/2. One weighting coefficient is used fourtimes within one cycle. FIG. 13 shows sampling points and an outputwaveform when the sampling points are selected so as to include both ofa maximum value and a zero cross. In this instance, n=k/2+1. A peakweighting coefficient and a maximum weighting coefficient are used onlytwice within one cycle. The other weighting coefficients are used fourtimes. Where the two cases are compared with each other, while thesampling of FIG. 12 requires two weighting coefficients, the sampling ofFIG. 13 requires three weighting coefficients including zero. Further,also the pulse signal for changing over the coefficient of the weightingcircuit 10 can be generated more readily for the sampling of FIG. 12.Accordingly, it is reasonable to arrange sampling points so as not toinclude any of a maximum value and a zero cross.

If the relative merits of k=3 and k=4, that is, six-time sampling andeight-time sampling, are considered, then the eight-time sampling of k=4is superior. This is because a sine wave signal having a higher samplingfrequency, that is, having a higher degree of accuracy, can be generatedusing same two weighting circuits 10.

Even if k further increases, the same basic rule applies. Where k is anodd number, sampling points including one of a maximum value and a zerocross are selected. The arrangement of sampling points which include azero cross is rather reasonable. The number n of necessary weightingcoefficients/circuits is a number obtained by rounding up k/2. Where kis an even number, either sampling points which does not include any ofa maximum value and a zero cross are selected or sampling points whichinclude both of them are selected. The number n of necessary weightingcoefficients/circuits is k/2. Irrespective of whether k is an odd numberor an even number, if a zero cross point is selected, then one of theweighting coefficients is zero.

Unless a special reason is applicable, it is most reasonable to set thesampling number k within one half cycle to an odd number and select suchsampling points which do not include any of a maximum value and a zerocross and are symmetrical with respect to a line where a maximum valueis selected but with respect to a point where a zero cross is selected.Further, k^(2i) (i is an integer) is useful including easiness in pulsegeneration. In particular, eight-time sampling of k=4, 16-time samplingof k=8 and 32-time sampling of k=16 are considered useful in practicaluse.

It is to be noted that the weighting circuit 10 uses a number ofweighting coefficients which is greater than 1 and is further greaterthan n-2 at least twice within one half cycle of a sine wave signal. Inparticular, since n is equal to or greater than 2, in the case of n=2 orn=3, one or more weighting coefficients are used at least twice withinone half cycle of the sine wave signal, and in the case of n=4 or more,2 (=4−2) or more weighting coefficients are used at least twice withinone half cycle of the sine wave signal.

CIRCUIT EXAMPLE 1

Now, particular circuit examples of the weighting circuit 10 and thepolarity changeover circuit 13 are described. FIG. 14 shows a circuitexample (circuit example 1) which has two addition coefficients andoperates with k=4, that is, eight-time sampling.

Various methods are applicable to implement the weighting circuit 10 andthe polarity changeover circuit 13. In FIG. 14, a circuit example whichuses an operational amplifier OP having differential inputs/outputs isshown. Where the weighting circuit 10 and the polarity changeovercircuit 13 are implemented using differential inputs/outputs in thismanner, they can be implemented very simply. In particular, theweighting circuit 10 and the polarity changeover circuit 13 can beformed from a resistor network 21 including resistors R1 and R2 and aswitch circuit 22 including switches SWm, SWp and SWpx. The switch SWmis used to change over the weighting coefficient, and the switches SWpand SWpx are used to change over the polarity. The switch SWpx operateswith the opposite polarity to that of the Switch SWp.

FIG. 15 illustrates control of the switches SWp and SWm and thecoefficients m1, m2, −m1 and −m2. When the switch SWm is on, theweighting coefficient depends upon an inverse number to the resistancevalue of the resistors R1 and provides m1 or −m1. When the switch SWm isoff, the weighting coefficient depends upon an inverse number to theresistors R1+R2 and provides m2 or −m2. The switches SWm, SWp and SWpxare implemented representatively by a CMOS switch.

Where the weighting circuit 10 and the polarity changeover circuit 13have such a circuit configuration that they are formed from the resistornetwork 21 and the switch circuit 22 and a weighting coefficient isobtained by changing over the transmission gain by means of the switchesSWm, SWp and SWpx, there is an advantage that an offset or an error of acoefficient can be suppressed to a very low value when compared withthose where they are formed using a transistor as in the Gilbert typemultiplier of the prior art described hereinabove.

CIRCUIT EXAMPLE 2

FIG. 16 shows a particular circuit example (circuit example 2) of theweighting circuit 10 and the polarity changeover circuit 13 where k=8,that is, for 16-time sampling. FIG. 17 illustrates control of switchesand weighting coefficients in the case of the circuit example 2.Switches SWp and SWpx for changing over the polarity are same as thosein the circuit example 1. In the present circuit example, threedifferent types of switches SWma, SWmb and SWmcx are used in order tochange over the weighting coefficient among four different weightingcoefficients.

When to provide a maximum weighting coefficient m1, the switches SWmaand SWmb are on and the switch SWmcx is off. If the switches SWma areturned off in this state, then the weighting coefficient m2 is provided,and if the switches SWmb are turned off further, then the weightingcoefficient m3 is provided. If the switch SWmcx is turned on further,then the minimum weighting coefficient m4 is provided. Since theswitches SWma, SWmb and SWmc are represented in FIG. 17 such that theweighting coefficient increases when any of them is on, two resisters R4in FIG. 16 are short-circuited, and the switch SWmcx is used as a switchfor lowering the weighting coefficient and it is represented such thatthe switch SWmcx exhibits an off state when the switch SWmc of FIG. 17exhibits an on state.

Now, different measures for implementing the weighting circuit 10 andthe polarity changeover circuit 13 are described.

Where an MOS device can be used, such measures which use the resistornetwork 21 and the switch circuit 22 as shown in FIG. 14 or 16 are mosteasy to implement and allow achievement of a good result. However, whereonly a bipolar device can be used, bidirectional switches like MOSswitches cannot be implemented simply. In such an instance, theweighting circuit 10 and the polarity changeover circuit 13 can beimplemented using a buffer circuit which equivalently has an inputswitch function.

CIRCUIT EXAMPLE 3

FIG. 18 shows a circuit example (circuit example 3) implemented by abuffer circuit equivalently having an input switch function.

Referring to FIG. 18, the sine wave multiplication circuit according tothe circuit example 3 includes a buffer amplifier 23 having two inputsto which potentials as nodes N1 and N2 of a resistor network 21A formedfrom three resistors connected in series between an input in+ to thesine wave multiplication circuit and the ground. The sine wavemultiplication circuit further includes another buffer amplifier 24having two inputs to which potentials at nodes N3 and N4 of anotherresistor network 21B formed from three resistors connected in seriesbetween the other input in− to the sine wave multiplication circuit andthe ground. The sine wave multiplication circuit further includes afurther buffer amplifier 25 having two inputs to which outputs of thebuffer amplifiers 23 and 24 are inputted, and a still further bufferamplifier 26 having two inputs to which the outputs of the bufferamplifiers 23 and 24 are inputted.

Each of the buffer amplifiers 23 to 26 includes switches at two inputstages thereof. Each of the buffer amplifiers 23 to 26 with an inputswitch function can be implemented, for example, by a buffer amplifierwhich can select and extract one of input signals IN1 and IN2 at anoutput OUT thereof by changing over the current of transistors Q5 and Q6to activate first differential pair transistors Q1 and Q2 or activatesecond differential pair transistors Q3 and Q4.

In the following, applications of the present invention are described.

Application 1

FIG. 20 shows an example of a configuration of a sine wavemultiplication circuit which uses the circuit example 2 (FIG. 16) as theweighting circuit 10 and the polarity changeover circuit 13 to generatea sine wave signal having a very high degree of amplitude accuracy. Inthe sine wave multiplication circuit of the present configurationexample, the amplitude of the output can be set with a high degree ofaccuracy by providing an amplitude control voltage Vc across the inputsin + and in− so that the amplitude of the output is controlled with theamplitude control voltage Vc. A clock having a frequency equal to eighttimes the frequency f of the sine wave signal to be used formultiplication is inputted to a pulse generation circuit 14. The pulsegeneration circuit 14 generates a switch control pulse illustrated inFIG. 17 based on the clock of the frequency equal to eight times thefrequency f. Also it is possible to achieve amplitude modulation with ahigh degree of accuracy if an arbitrary signal is applied to theamplitude control voltage Vc.

Application 2

FIG. 21 shows an example of a configuration of a sine wavemultiplication circuit according to an application 2 wherein an inputcomplex signal is multiplied by a complex signal of a frequency f.

As can be seen apparently from FIG. 21, the sine wave multiplicationcircuit according to the present application 2 includes a multiplicationcircuit 31 to which a first analog signal VR(t) is inputted, anothermultiplication circuit 32 to which a second analog signal VI(t) isinputted, and a Cos pulse generation circuit 33 and a Sin pulsegeneration circuit 34 serving as a control section for controlling themultiplication circuits 31 and 32. The sine wave multiplication circuitfurther includes an addition circuit 35 for receiving an output signalOUT+ of the multiplication circuit 31 as an addition input and receivingan output signal OUT+ of the multiplication circuit 32 as a subtractioninput, and another addition circuit 36 for receiving the other outputOUT− of the multiplication circuit 31 as an addition input and receivingthe other output OUT− of the multiplication circuit 32 as a subtractioninput.

In the sine wave multiplication circuit according to the application 2having the configuration described above, for example, the sine wavemultiplication circuit according to the circuit example 2 of FIG. 16 isused as it is as the multiplication circuit 31 and the multiplicationcircuit 32. The Cos pulse generation circuit 33 and the Sin pulsegeneration circuit 34 generate a Cos signal and a Sin signal,respectively, which have phases displaced by n/2 from each other basedon a clock clk having a frequency of 8f and control the weightingcoefficients of the multiplication circuits 31 and 32 so that outputsignals of the multiplication circuits 31 and 32 may be orthogonal toeach other.

Where the input signal is represented by Ase^(jωst) and the clock isrepresented by e^(jωst), the sine wave multiplication circuit accordingto the application 2 executes the following arithmetic operation:Re[Ase ^(jωst) e^(jωct)]=Cos(ωst)·Cos(ωct)−Sin(ωst)·Sin(ωct)=Cos{(ωs+ωc)t}  (3)

This is determination of the real part of complex multiplication of twocomplex frequencies. Also it is possible to prepare another sine wavemultiplication circuit according to the application 2 to add a circuitfor performing multiplication of the real part and the imaginary part sothat a full complex output can be obtained.

A frequency of a sum or a difference can be generated accurately byperforming complex multiplication of sine wave signals in this manner.Although such multiplication is possible with a conventional analogmultiplication circuit such as, for example, an analog multiplier calledGilbert type, the conventional analog multiplication circuit is not verypractical because the feed-through, image and so forth of a signal arevery high from the problems of the offset voltage, linearity, dynamicrange and so forth. In contrast, where the multiplication circuitaccording to the present invention is used, multiplication of a veryhigh degree of accuracy can be achieved.

Furthermore, although multiplication of a sine wave signal and an analogsignal is a basic function of signal processing, the multiplicationcircuit of the present invention can achieve implementation of a processwhich cannot conventionally be placed into practical use from arestriction to the performance of an analog multiplication circuit. Forexample, where a desired signal exists at a frequency fo and adisturbance signal exits at the frequency −fo in a complex signal asseen in FIG. 22, implementation of extraction only of the frequency foby an analog circuit is restricted very much in terms of performance.However, according to the present invention, since complexmultiplication of an arbitrary frequency can be performed with a veryhigh degree of accuracy, it is possible to down convert the frequency fointo dc current or covert the frequency fo into an arbitrary frequencyreadily while minimizing the influence of a disturbance wave of thefrequency −fo of an image component. Thus, the possibility of signalprocessing by an analog circuit can be expanded significantly.

While a preferred embodiment of the present invention has been describedusing specific terms, such description is for illustrative purposesonly, and it is to be understood that changes and variations may be madewithout departing from the spirit or scope of the following claims.

1. A sine wave multiplication circuit for multiplying an analog signalby a sine wave signal, comprising: a weighting section having nweighting coefficient each having a unique value for multiplying theanalog input signal by the weighting coefficients, n being an integerequal to or greater than 2; a polarity changeover section for changingover the polarity of the analog input signal outputted from saidweighting section after multiplied by one of the n weightingcoefficients; and a control section for performing changeover among then weighting coefficients and changeover of the polarity after everysampling period equal to ½k of one period of the sine wave signal bywhich the analog input signal is multiplied, k being an integer, 2kbeing equal to or greater than 6 but equal to or smaller than 4n.
 2. Asine wave multiplication circuit according to claim 1, wherein theweighting coefficient and the polarity are set so that the product ofthe weighting coefficient and the polarity after the changeover afterevery sampling period increases in proportion to an instantaneous valueof the sine wave signal at instantaneous time after every samplingperiod.
 3. A sine wave multiplication circuit according to claim 1,wherein said weighting section uses a number of ones of the weightingcoefficients which is equal to or greater than 1 and is equal to orgreater than n−2 at least twice within one half period of the sine wavesignal.
 4. A sine wave multiplication circuit according to claim 1,wherein said weighting section and said polarity changeover section areformed from a resistor network and a switch element such that atransmission gain is changed over by said switch element.
 5. A sine wavemultiplication circuit according to claim 1, wherein said weightingsection multiplies positive and negative inputs by a same one of theweighting coefficients, and said polarity changeover section extractsthe positive and negative inputs given thereto from said weightingsection as a positive phase output and an opposite phase output thereof.6. A sine wave multiplication circuit, comprising: a firstmultiplication section formed from the sine wave multiplication circuitaccording to claim 1 for receiving a first analog signal as an inputthereto; a second multiplication section formed from the sine wavemultiplication circuit according to claim 1 for receiving a secondanalog signal as an input thereto; a control section including a Cospulse generation circuit and a Sin pulse generation circuit forcontrolling weighting coefficients of said first and secondmultiplication sections so that output signals of said first and secondmultiplication sections are orthogonal to each other; and an additionsection for adding the output signals of said first and secondmultiplication sections.
 7. A sine wave multiplication circuit accordingto claim 1, wherein the sampling number 2k within one cycle is 2(2n−1),and the n weighting coefficients include a maximum value but do notinclude a zero cross within a positive half cycle of the sine wavesignal and are set so as to be equal to instantaneous values of the sinewave signal where the n weighting coefficients are selected at intervalsof time equal to 1/(2n−1) of one half cycle of the sine wave signal in asymmetrical relationship with respect to time at which the sine waveexhibits the maximum value.
 8. A sine wave multiplication circuitaccording to claim 1, wherein the sampling number 2k within one cycle is2(2n−1) and one of the n weighting coefficients is zero, and the nweighting coefficients do not include a maximum value but include a zerocross within a positive half cycle of the sine wave signal and are setso as to be equal to instantaneous values of the sine wave signal wherethe n weighting coefficients are selected at intervals of time equal to1/(2n−1) of one half cycle of the sine wave signal in a symmetricalrelationship with respect to time at which the sine wave exhibits themaximum value.
 9. A sine wave multiplication circuit according to claim1, wherein the sampling number 2k within one cycle is 4n, and the nweighting coefficients do not include any of a maximum value and a zerocross within a positive half cycle of the sine wave signal and are setso as to be equal to instantaneous values of the sine wave signal wherethe n weighting coefficients are selected at intervals of time equal to½n of one half cycle of the sine wave signal in a symmetricalrelationship with respect to time at which the sine wave exhibits themaximum value.
 10. A sine wave multiplication circuit according to claim1, wherein the sampling number 2k within one cycle is 2(2n−2) and one ofthe n weighting coefficients is zero, and the n weighting coefficientsinclude both of a maximum value and a zero cross within a positive halfcycle of the sine wave signal and are set so as to be equal toinstantaneous values of the sine wave signal where the n weightingcoefficients are selected at intervals of time equal to 1/(2n−2) of onehalf cycle of the sine wave signal in a symmetrical relationship withrespect to time at which the sine wave exhibits the maximum value.
 11. Asine wave multiplication method for multiplying an analog signal by asine wave signal, comprising: a first step of multiplying the analoginput signal by n weighting coefficient each having a unique value, nbeing an integer equal to or greater than 2; a second step of changingover the polarity of the analog input signal multiplied by one of the nweighting coefficients; and a third step of performing changeover amongthe n weighting coefficients and changeover of the polarity after everysampling period equal to ½k of one period of the sine wave signal bywhich the analog input signal is multiplied, k being an integer, 2kbeing equal to or greater than 6 but equal to or smaller than 4n.
 12. Asine wave multiplication method according to claim 11, wherein theweighting coefficient and the polarity are set so that the product ofthe weighting coefficient and the polarity after the changeover afterevery sampling period increases in proportion to an instantaneous valueof the sine wave signal at instantaneous time after every samplingperiod.
 13. A sine wave multiplication method according to claim 11,wherein, at the first step, a number of ones of the weightingcoefficients which is equal to or greater than 1 and is equal to orgreater than n−2 are used at least twice within one half period of thesine wave signal.
 14. A sine wave multiplication method according toclaim 11, wherein the sampling number 2k within one cycle is 2(2n−1),and the n weighting coefficients include a maximum value but do notinclude a zero cross within a positive half cycle of the sine wavesignal and are set so as to be equal to instantaneous values of the sinewave signal where the n weighting coefficients are selected at intervalsof time equal to 1/(2n−1) of one half cycle of the sine wave signal in asymmetrical relationship with respect to time at which the sine waveexhibits the maximum value.
 15. A sine wave multiplication methodaccording to claim 11, wherein the sampling number 2k within one cycleis 2(2n−1) and one of the n weighting coefficients is zero, and the nweighting coefficients do not include a maximum value but include a zerocross within a positive half cycle of the sine wave signal and are setso as to be equal to instantaneous values of the sine wave signal wherethe n weighting coefficients are selected at intervals of time equal to1/(2n−1) of one half cycle of the sine wave signal in a symmetricalrelationship with respect to time at which the sine wave exhibits themaximum value.
 16. A sine wave multiplication method according to claim11, wherein the sampling number 2k within one cycle is 4n, and the nweighting coefficients do not include any of a maximum value and a zerocross within a positive half cycle of the sine wave signal and are setso as to be equal to instantaneous values of the sine wave signal wherethe n weighting coefficients are selected at intervals of time equal to½n of one half cycle of the sine wave signal in a symmetricalrelationship with respect to time at which the sine wave exhibits themaximum value.
 17. A sine wave multiplication method according to claim11, wherein the sampling number 2k within one cycle is 2(2n−2) and oneof the n weighting coefficients is zero, and the n weightingcoefficients include both of a maximum value and a zero cross within apositive half cycle of the sine wave signal and are set so as to beequal to instantaneous values of the sine wave signal where the nweighting coefficients are selected at intervals of time equal to1/(2n−2) of one half cycle of the sine wave signal in a symmetricalrelationship with respect to time at which the sine wave exhibits themaximum value.